A polynomial upper bound on Reidemeister moves

Author: 

Lackenby, M

Publication Date: 

September 2015

Journal: 

Annals of Mathematics

Last Updated: 

2019-08-25T07:59:32.893+01:00

Issue: 

2

Volume: 

182

page: 

491-564

abstract: 

We prove that any diagram of the unknot with c crossings may be reduced to
the trivial diagram using at most (236 c)^{11} Reidemeister moves. Moreover,
every diagram in this sequence has at most (7 c)^2 crossings. We also prove a
similar theorem for split links, which provides a polynomial upper bound on the
number of Reidemeister moves required to transform a diagram of the link into a
disconnected diagram.

Symplectic id: 

384391

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article